This paper shows that in macroeconomic models of product differentiation that are built on CES utility specifications the widely used assumption of approximating cross price effects to zero, (since Dixit-Stiglitz 1979), plays indeed no crucial role. This is true not only when a large number of agents is assumed, but also at the flexible symmetric macro equilibrium where such effects are shown to cancel out regardless of the number of agents. We then show that this latter result is no longer true in the presence of nominal rigidities, where the ratio of cross to own price elasticities, (typically absent in recent New Keynesian models), is shown to be the key determinant of the coefficient of wage and inflation persistence.
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